Can Standard Deviation Be Negative? No (See Why)

In one word: No.

Why Standard Deviation Can’t Be Negative

First, let’s stop for a moment and think about what standard deviation represents.

It measures variability in a data set.

When you have some set of numbers and calculate its standard deviation, the resulting number tells you to what extent the individual numbers in the set are different from each other. If all are about the same (like 252, 249, 253, 251, 254), standard deviation will be relatively small. If there are big differences (like 252, 11, 840, 305, 64, 5846), standard deviation will be much bigger.

What if all the numbers in the data set are exactly the same (like 252, 252, 252, 252, 252, 252)? Then standard deviation will be exactly zero.

Can you get an even smaller standard deviation (which would have to be negative)? No. You can’t have a data set which is less diverse than one where all numbers are the same, right?

To conclude, the smallest possible value standard deviation can reach is zero. As soon as you have at least two numbers in the data set which are not exactly equal to one another, standard deviation has to be greater than zero – positive. Under no circumstances can standard deviation be negative.

Why Standard Deviation Can’t Be Negative Mathematically

The above was the common sense explanation. There is also a mathematical explanation, based on the way standard deviation is calculated.

Standard deviation is the square root of variance, which is the average squared deviation from the mean and as such (average of some squared numbers) it can’t be negative. See more detailed explanation here: Can variance be negative?

Related pages

sec 13f filingsoptions vixmeasures of skewness and kurtosisstandard deviation on financial calculatorge stock futuresblack shoelswacc computationoption payoff graphequation for skewnesscalculate derivative in exceloptions greek calculatornormal distribution excel templatedax index methodologystraddle strategy in optionseuro stoxx 50 quotecitibank reverse splitexponential moving average excel formulablack scholes inputshow to interpret sharpe ratioxxv etfpercentiles calculator statisticsipath barclaysdays calculator excelnotepad background colorcboe settlement pricesfinance tvixexcel variance formulafree black scholes calculatorshort payoff definitionnorm.s.distsample standard deviation calculatorvaluing a call optionsharpe ratio exampleshort straddle optionkurtosis and skewstd deviation definitionproshares short s&p 500 etfvix white papercalculating historical volatilitydividend calculator spreadsheetblack scholes options pricing modelhow is vxx calculatedimplied volatility vbavix futures symboloption trading bookformula for exponential moving averagehistorical volatility chartblack scholes calculationformula for kurtosis in statisticsformula of kurtosissma and emacalculate standard deviation using exceluvxy yahoo financej welles wilderwhat is straddle positionhedge fund holdings 13frsi overbought oversoldsharpe ratio calculatorhow to calculate exponential moving average in excelstandard deviation calculator with mean and sample sizeblack scholes formulablack scholes model formulacall spread payoffbroken wing iron condorreturns calculator excelshort term vixdifference between arbitrage and hedgingoptions implied volatility calculatorformula to calculate variance percentagehow to calculate median in excelyahoo stock csv